Essential norms of weighted composition operators between Hardy spaces $H^p$ and $H^q$ for $1<= p,q<=infty$.

16 pagesWe complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^p$ and $H^q$ for $1<= p,q<=\infty.$ In particular, we give some estimates for the cases $1=p <= q <=\infty$ and $1<=